Ranked Choice Star Voting ?
Why is this a bad idea?
Voters score 0 through 5, like in star voting. The two lowest-scored candidates are then compared head-to-head in terms of who voters preferred. The loser is removed from the vote and the process is repeated like in ranked-choice voting.
To me, this seems like a more accurate version of star voting. Am I missing something?
@sander this is a reasonable and interesting hybrid between score voting and Tideman’s bottom-two runoff, which is a nice rank-order single-winner system. I think it may have some merit, and should be analyzed carefully. Even though it sounds reasonable, though, it isn’t something canonical or “more accurate” necessarily. In any case, it is definitely not a bad idea. It sits somewhere in the spectrum of voting systems and it has its own unique set of properties.
This is something similar in spirit, but it has its own non-canonical aspects, some of which perhaps mirror certain aspects of your system:
Generally, these kinds of “step-wise elimination” systems have to computationally define, in some manner, the properties that determine which candidate is to be eliminated at any given step. But what those properties should be, or even whether step-wise elimination is desired in the first place, is not a choice that can be easily made in a “universal” way. Loosely speaking, one can almost always make the properties “more” universal in some specific sense.
My motivation for the above system was that, rather than looking at the loser in a bottom pair, if there is a Condorcet loser in a bottom triple, or quadruple, etc., they “should” be eliminated with higher priority. This is ultimately just a different way to decide how to break Condorcet cycles with the goal of preserving a higher degree of monotonicity. But the system I proposed above uses only ordinal ranks, whereas yours is enriched with cardinal scores, and each approach naturally comes with pros and cons.
The main thing to watch out for in any modification of score voting is "does this create an incentive for turkey-raising." Turkey-raising is when a tactical voter raises bad candidates ("turkeys") above last place / zero score. It's extremely bad and it's infamous for ruining the Borda Count.
Score voting itself does not have turkey-raising (there's never a reason to give bad candidates anything other than 0). STAR doesn't have it either, because it's a combination of two methods that don't (score voting and some kind of automatic two-round system.)
This method looks like a combination of score voting and BTR. BTR has turkey-raising. There's an incentive to put turkeys ahead of a competitive rival in order to increase the rival's chance of being eliminated. So this method might have turkey-raising as well.
@isocratia interesting. The system I mention above is also susceptible to Turkey-raising but is probably more resistant to it than the STAR-BTR. There’s a sort of dual to it which might be even more resistant:
First define a sequence of “quality” functions Q_k over the candidates. For example, Q_k could be the number of first-place rankings, even conditional on eliminations.
(1) Let N be the number of candidates, and set k=1.
(2) If X is a Condorcet winner among the N candidates with the highest Q_k value, elect X.
(3) Otherwise, reduce N by 1, increase k by 1, and repeat from (2).
If we also take care of Condorcet losers along the way it can become even more robust.
I've heard that it's possible to make some Condorcet methods immune to turkey-raising by designing for a property called "dominant mutual third burial resistance." But I'm not familiar with examples of methods that do this, and it's been hard to find information about it. And in any case approval and score voting solve this problem in a much less complicated way.
@isocratia I’m not sure how score and approval can be said to solve the problem of burial at all, if one considers bullet voting to be a form of it. And the flexibility leaves a ton of room for regret and dissatisfaction with a voter’s choice of ballot.
I’ve personally come to feel that enabling “strength of preference” indications in whatever form isn’t actually worth the cost. No matter what “strength of preference” actually is, on aggregate it makes sense for it to regress to something normative.
IMO, instead of using cardinals to measure gaps between candidates, the public should bridge those gaps with reasonable alternative candidates who can compromise between platforms.
@sander, sequential bottom two runoff, is a Smith efficient Condorcet procedure. It will always select a member of the Smith set and the Condorcet winner if there is one. Though the procedure you describe is different, it will produce the same results as Smith//Score. With score relegated to the relatively trivial role of cycle breaking, properties of Condorcet systems will predominate. By contrast the top two runoff of STAR will block a Condorcet loser, but a Condorcet winner can still lose if they don't get a good enough score to get in the runoff. This is enough for STAR to retain some significant properties of Score.
Bullet voting is not the dominant strategy in score voting or approval voting for that matter. The dominant strategy is to identify the top 2 frontrunners, max-score the one you prefer, and min-score the other one. Then you max-score anyone else you like more than the frontrunner you just max scored. For some voters, that's a bullet vote, but not all.
If everyone uses this strategy, it elects the actual Condorcet winner. That's a theorem that's been independently discovered by several mathematicians.
@isocratia surely it can only elect the Condorcet winner if one exists. Can you cite this theorem?
@isocratia I’m not sure how score and approval can be said to solve the problem of burial at all, if one considers bullet voting to be a form of it.
I think burying is generally seen as putting a candidate underneath other preferred candidates. Normally in score/approval they'd be equally scored zero or unapproved.